Question

САМОСТАЯТЕЛЬНАЯ РАБОТА Одна бригада может закончить ремонт дороги длиной 900км за 30 дней,а другая эту же работу выполнят за 45 дней.За сколько времени завершат эту работу обе бригады, если будут работать одновременно с двух сторон дороги и с той же производительностью?Краткая запись тоже нужна!​

Answer 1

Ответ:

18 дней

Пошаговое объяснение:

900:30=30

900:45=20

20+30=50

900:50=18

Answer 2

Problem Analysis

We are given that one brigade can complete the repair of a 900 km road in 30 days, while another brigade can complete the same work in 45 days. We need to determine how long it will take for both brigades to complete the work if they work simultaneously from both sides of the road and maintain the same productivity.

Solution

To solve this problem, we can use the concept of work rates. The work rate is defined as the amount of work done per unit of time. In this case, the work rate is measured in kilometers per day.

Let's assume that the work rate of the first brigade is x kilometers per day and the work rate of the second brigade is y kilometers per day.

According to the given information, the first brigade can complete the work in 30 days, so we can write the equation: x * 30 = 900 (equation 1)

Similarly, the second brigade can complete the work in 45 days, so we can write the equation: y * 45 = 900 (equation 2)

We need to find the time it takes for both brigades to complete the work when they work simultaneously. Since they are working from both sides of the road, their work rates will add up.

Let's assume that it takes t days for both brigades to complete the work when working simultaneously. The combined work rate of both brigades will be x + y kilometers per day.

According to the given information, the total length of the road is 900 km. Therefore, we can write the equation: (x + y) * t = 900 (equation 3)

To solve this system of equations, we can use substitution or elimination.

Solution using Substitution

We can solve equations 1 and 2 for x and y, respectively, and substitute the values into equation 3.

From equation 1, we have: x = 900 / 30 = 30 (equation 4)

From equation 2, we have: y = 900 / 45 = 20 (equation 5)

Substituting equations 4 and 5 into equation 3, we get: (30 + 20) * t = 900 50t = 900 t = 900 / 50 = 18

Therefore, both brigades will complete the work in 18 days when working simultaneously.

Solution using Elimination

We can subtract equation 2 from equation 1 to eliminate y.

From equation 1, we have: x = 900 / 30 = 30 (equation 4)

From equation 2, we have: y = 900 / 45 = 20 (equation 5)

Subtracting equation 5 from equation 4, we get: x - y = 30 - 20 = 10 (equation 6)

Now, we can substitute equation 6 into equation 3 and solve for t.

(x + y) * t = 900 (x + y) * t = (x - y) * t + 2y * t 900 = 10t + 2y * t 900 = 10t + 2 * 20 * t 900 = 10t + 40t 900 = 50t t = 900 / 50 = 18

Therefore, both brigades will complete the work in 18 days when working simultaneously.

Conclusion

Both brigades will complete the repair of the 900 km road in 18 days when working simultaneously from both sides of the road and maintaining the same productivity.

Note: The sources provided do not contain specific information related to this problem. The solution is derived using mathematical concepts and equations.